We’re now going to re-create the old exercise of drawing an ellipse using a pencil, two pins, and a piece of string.
- Turn on the axes by clicking on the grid tool in the toolbar.
- Make two line segments, AB and BC. Points A and C are the pins, while B represents the pencil.
- Select point A.
- Add an input constraint of type Coordinate to set the coordinates of the point.
- When the constraint highlights, enter (not forgetting the parentheses):
(-a,0)
- Select point C and constrain its coordinates to be at (a,0).
- Scroll down, if necessary, to see the value of a in the Variables palette.
- Reselect A and drag it to the right a short distance. As you drag, notice:
- A is now constrained to lie along the X axis; moving it up or down has no effect.
- When you move A, C also moves.
- When you move A, the value of the associated variable a changes in the Variables list.
- Select the line AB and constrain its length to be distance t.
- Select the line BC and constrain its length to be L–t. L now represents the length of the string.
- Notice that the two new variables have appeared in the Variables list.
- Select B.
- In the Construct palette, select Locus to construct a locus through B.
- In the resulting dialog, choose t as the parameter to vary, and enter start and end values of 0–25, guesses that will probably produce a complete curve.
The locus appears — half of an ellipse, above the X axis.
- Now drag B up and down, the equivalent of changing the length of the string, and seeing how the ellipse changes. You can also drag A or C to change the position of the pins.
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